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Relations for zeros of special polynomials associated to the Painleve equations
Nikolai A. Kudryashov, Maria V. Demina
A method for finding relations for the roots of polynomials is presented. Our approach allows us to get a number of relations for the zeros of the classical polynomials and for the…
Power expansions for the self-similar solutions of the modified Savada-Kotera equation
Olga Yu. Efimova, Nikolai A. Kudryashov
The fourth-order ordinary differential equation, defining new transcendents, is studied. The self-similar solutions of the Kaup-Kupershmidt and Savada-Kotera equations are shown to…
Newton polygons for finding exact solutions
Nikolai A. Kudryashov, Maria V. Demina
A method for finding exact solutions of nonlinear differential equations is presented. Our method is based on the application of the Newton polygons corresponding to nonlinear diff…
Special polynomials associated with the fourth order analogue to the Painlev'e equations
Nikolai A. Kudryashov, Maria V. Demina
Rational solutions of the fourth order analogue to the Painlev'e equations are classified. Special polynomials associated with the rational solutions are introduced. The structure…
The Yablonskii - Vorob'ev polynomials for the second Painlev'e hierarchy
Maria V. Demina, Nikolai A. Kudryashov
Special polynomials associated with rational solutions of the second Painlev'e equation and other equations of its hierarchy are studied. A new method, which allows one to construc…
Mathematical model for blood flow autoregulation by endothelium-derived relaxing factor
Igor L. Chernyavsky, Nikolai A. Kudryashov
The fluid shear stress is an important regulator of the cardiovascular system via the endothelium-derived relaxing factor (EDRF) that is Nitric Oxide. This mechanism involves bioch…
Explicit form of the Yablonskii - Vorob'ev polynomials
Maria V. Demina, Nikolai A. Kudryashov
Special polynomials associated with rational solutions of the second Painlevé equation and other members of its hierarchy are discussed. New approach, which allows one to construct…
Polygons for finding exact solutions of nonlinear differential equations
Nikolai A. Kudryashov, Maria V. Demina
New method for finding exact solutions of nonlinear differential equations is presented. It is based on constructing the polygon corresponding to the equation studied. The algorith…